Absorption - Introduction to Carbon Capture and Sequestration - page 202

Question 5.4.1 Diffusion or reaction

In the diffusion-limited equation we see the reaction rate, in the reaction-limited
equation we see the diffusion coeffi cient. Does this make sense?

From the boundary conditions we have:

( ) ( )

∗ 0 ∗ 0

c − c exp − k L ′ c − c exp − k L ′

CO CO

CO CO 2 2

A =

2

=

2

( ) ( ) ( )

exp kL ′ − exp − kL ′ 2 sin h − kL ′

( ) ( )

∗ 0 ∗ 0

c − c exp k L ′ − c + c exp k L ′

CO CO

CO CO

2 2

2 2

B = =

( ) ( ) ( )

exp kL ′ − exp − kL ′ 2 sin h kL ′

The fl ux is given by:

( ) ( )

()

j z =− DAk ′ exp k z ′ − Bk ′ exp − k z ′

CO CO

2 2

Of particular interest is the fl ux at z = 0:

()

[ ]

j 0 =− D k ′ A − B

CO CO

2 2

Dk ′

( )

( )

CO

0 ∗ 2

c cos h k L c

= ′ −

( )

CO

CO 2

sin hkL ′

2

This equation looks complex, but we can learn a lot by looking at two
limiting cases.
Let us fi rst assume that the reaction is slow compared to diffusion:

kc

rB

kL ′ = L 1

D

CO

2